The method of operational matrices based on different types of polynomials such as Bernstein, shifted Legendre and Bernoulli polynomials will be presented and implemented to solve the nonlinear Blasius equations approximately. The nonlinear differential equation will be converted into a system of nonlinear algebraic equations that can be solved using Mathematica®12. The efficiency of these methods has been studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as the polynomial degree (n) increases, since the errors decrease. Moreover, the approximate solutions obtained by the proposed methods are compared with the solution of the 4th order Runge-Kutta method (RK4), which gives very good agreement. In addition, the convergence of the proposed approximate methods is given based on one of the Banach fixed point theorem results.
This paper reports the synthesis and use of a novel metal-organic framework (MOF), named Zr-BADS, within the thin-film nanocomposite (TFN) membranes for reverse osmosis (RO) applications. Two types of zirconium-based MOFs, Zr-BADS-1 and Zr-BADS-2, were synthesized via a solvothermal method using bicinchoninic acid disodium salt as a linker and either dimethylformamide or ethanol as solvent, respectively. TFN membranes were prepared by embedding these MOFs within the polyamide thin film supported by a polysulfone support sheet. The specific surface area of Zr-BADS-1 and Zr-BADS-2 was determined to be 396.1 and 278.6 m2/g, respectively, indicating significant surface area conducive to water permeation. Scanning electron microscopic analysis r
... Show MoreThis study used deep eutectic solvent (DES) as the liquid membrane in a bulk liquid membrane system (BLM) to remove glycerol from waste cooking oil‐based biodiesel. The DES was prepared from choline chloride and tetraethylene glycol at a molar ratio of 1:5. Diethyl ether was employed as a novel strip phase for the glycerol in BLM. The effects of the DES: biodiesel ratio, stirring speed, and extraction time on the extraction and stripping efficiencies were investigated. The results showed that BLM could give better glycerol removal from biodiesel than mechanical shaking. Increasing the DES: biodiesel ratio, stirring speed, and extraction time can enhance glycerol removal from the feed phase, achievi
A novel demountable shear connector for precast steel-concrete composite bridges is presented. The connector uses high-strength steel bolts, which are fastened to the top flange of the steel beam with the aid of a special locking nut configuration that prevents bolts from slipping within their holes. Moreover, the connector promotes accelerated construction and overcomes the typical construction tolerance issues of precast structures. Most importantly, the connector allows bridge disassembly. Therefore, it can address different bridge deterioration scenarios with minimum disturbance to traffic flow including the following: (1) precast deck panels can be rapidly uplifted and replaced; (2) connectors can be rapidly removed and replaced; and (
... Show MoreThe aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.
In this paper, a new analytical method is introduced to find the general solution of linear partial differential equations. In this method, each Laplace transform (LT) and Sumudu transform (ST) is used independently along with canonical coordinates. The strength of this method is that it is easy to implement and does not require initial conditions.
Oscillation criteria are obtained for all solutions of the first-order linear delay differential equations with positive and negative coefficients where we established some sufficient conditions so that every solution of (1.1) oscillate. This paper generalized the results in [11]. Some examples are considered to illustrate our main results.
In this paper, we consider inequalities in which the function is an element of n-th partially order space. Local and Global uniqueness theorem of solutions of the n-the order Partial differential equation Obtained which are applications of Gronwall's inequalities.
We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.